Siberian Mathematical Journal

, Volume 47, Issue 2, pp 376–382 | Cite as

Multidimensional exact solutions to a quasilinear parabolic equation with anisotropic heat conductivity

  • E. I. Semenov


We prove invariance of a quasilinear parabolic equation with anisotropic heat conductivity in the three-dimensional coordinate space under some equivalence transformations and present some explicit formulas for these transformations. We consider nontrivial reductions of the equation to similar equations of less spatial dimension. Using these results, we construct new exact multidimensional solutions to the equation which depend on arbitrary harmonic functions.


quasilinear parabolic heat equation Liouville equation multidimensional exact solution equivalence transformation anisotropy conjugate harmonic function 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • E. I. Semenov
    • 1
  1. 1.Institute of System Dynamics and Control TheoryIrkutskRussia

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